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A Recursive Eigenspace Computation for the Canonical Polyadic Decomposition

The canonical polyadic decomposition (CPD) is a compact decomposition which expresses a tensor as a sum of its rank-1 components. A common step in the computation of a CPD is computing a generalized eigenvalue decomposition (GEVD) of the tensor. A GEVD provides an algebraic approximation of the CPD which can then be used as an initialization in optimization routines. While in the noiseless setting GEVD exactly recovers the CPD, it has recently been shown that pencil-based computations such as GEVD are not stable. In this article we present an algebraic method for approximation of a CPD which greatly improves the accuracy of GEVD. Our method is still fundamentally pencil based; however, rather than using a single pencil and computing all of its generalized eigenvectors, we use many different pencils and in each pencil compute generalized eigenspaces corresponding to sufficiently well-separated generalized eigenvalues. The resulting “generalized eigenspace decomposition" is significantly more robust to noise than the classical GEVD. Accuracy of the generalized eigenspace decomposition is examined both empirically and theoretically. In particular, we provide a deterministic perturbation theoretic bound which is predictive of error in the computed factorization.

Ketersediaan

Informasi Detail

Judul Seri

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS; Vol.43 No.1 January-March 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 274-300

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

MULTIDIMENSIONAL ARRAYS
CANONICAL POLYADIC DECOMPOSITION
MULTILINEAR ALGEBRA
TENSORS
GENERALIZED EIGENVALUE DECOMPOSITION

Info Detail Spesifik

https://doi.org/10.1137/21M1423026

Pernyataan Tanggungjawab

Eric Evert, Michiel Vandecappelle, Lieven De Lathauwer

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